CVP verified calculation capability
Piecewise-linear, Lagrange, or natural cubic spline of tabulated (x, y). Not regression, not CAS.
Math · Numerical Capability ID math.numerical.interpolate version 1.1.4 CVP VERIFIED STALE Core
Linear
y = y₀ + (y₁−y₀)(x−x₀)/(x₁−x₀)y = Σ yⱼ ℓⱼ(x), ℓⱼ = Πᵢ≠ⱼ (x−xᵢ)/(xⱼ−xᵢ)S″(x₀) = S″(xₙ) = 0Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
method | — | — | input / output |
x | Abscissa at which to evaluate y | — | input / output |
points | x,y; x,y pairs | — | input |
x0 | — | — | input |
y0 | — | — | input |
x1 | — | — | input |
y1 | — | — | input |
extrapolate | If true, linear and spline use the end piece outside [x_min, x_max] | — | input |
y | — | — | output |
n | — | — | output |
x_min | — | — | output |
x_max | — | — | output |
in_range | — | — | output |
extrapolated | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | weighted piecewise linear / ordinate-normalized Lagrange with compensated summation / natural cubic spline with normalized coordinates and ordinates; exact node lookup before Lagrange or spline arithmetic; 12 significant digits without nonzero clamping |
valid_domain | strictly increasing abscissae; n in the published bound |
singularity_policy | INVALID_INPUT on duplicate x or too-few points; NUMERICAL_RANGE_ERROR on nonfinite table width or evaluated/published result |
branch_policy | not applicable — real iterate |
tolerance | not applicable — interpolant is determined by the nodes; query is float64 eval |
convergence | not applicable — direct factorization of the small spline system |
conditioning | high-degree Lagrange is ill-conditioned; spline is the published default for smoothness |
rounding | ieee754_round_ties_to_even |
overflow | ieee754_nonfinite_or_coded_error |
reproducibility | deterministic algorithm + Capability@Version |
independent_oracle | cvp:math.numerical.interpolate O2 / Evidence published cases |
golden_vectors | Evidence golden + boundary + property (and published_reference_case when listed) |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
One numerical check. The calculator page holds worked steps and FAQ.
linear (0,0)(10,20) x=5 → 10
CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Core assurance · all published methods. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.
Human page, REST, and MCP share the same engine and calculation_version.
Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json
and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 6/6.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/numerical-interpolation' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"method":"linear","points":"0,0; 10,20","x":5},"calculation_version":"1.1.4"}'{
"inputs": {
"method": "linear",
"points": "0,0; 10,20",
"x": 5
},
"calculation_version": "1.1.4"
}POST /api/v1/calc/numerical-interpolation. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Human-readable sources plus CVP reference evidence classes.
Sources
Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior
Inspect, then execute. Same engine as REST and the human calculator.
curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: inspect_capability' \
-d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.numerical.interpolate"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: execute_calculation' \
-d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.numerical.interpolate","inputs":{"method":"linear","points":"0,0; 10,20","x":5},"calculation_version":"1.1.4"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.1.4) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.